Empirical bond polarizability model for fullerenes

Abstract

The static polarizability properties and the Raman-scattering intensities in molecular ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ are found to be well reproduced by a bond polarizability model with parameters similar to those obtained from studies of hydrocarbons. For the Raman spectrum of ${\mathrm{C}}_{60}$ with off-resonance infrared laser excitation, a fit using first-principles vibrational eigenvectors yields ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}^{\ensuremath{'}}$-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}^{\ensuremath{'}}$=2.30 A${\mathrm{\r{}}}^{2}$, 2${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}^{\ensuremath{'}}$+${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}^{\ensuremath{'}}$=2.30 A${\mathrm{\r{}}}^{2}$, ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}$-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}$=1.28 A${\mathrm{\r{}}}^{3}$ for single bonds and ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}^{\ensuremath{'}}$-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}^{\ensuremath{'}}$=2.60 A${\mathrm{\r{}}}^{2}$, 2${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}^{\ensuremath{'}}$+${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}^{\ensuremath{'}}$=7.55 A${\mathrm{\r{}}}^{2}$, ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}$-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}$=0.32 A${\mathrm{\r{}}}^{3}$ for double bonds, with (${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\parallel}}}$-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{\perp}}}$) for the single bond arbitrarily set equal to its value in ethane, namely, 1.28 A${\mathrm{\r{}}}^{3}$. The transferability of these parameters to ${\mathrm{C}}_{70}$ is discussed in detail. \textcopyright{} 1996 The American Physical Society.